In this paper, we build off reduced order modeling techniques using the so-called Koopman operator [1]}, [2]}, [3]}, [4]}, [5]}. For any nonlinear dynamical systems, there is an associated (infinite-dimensional) linear operator that encodes the dynamics as a linear system [4]}, [5]}, [8]}. This operator is called the Koopman operator. In many cases, this linear operator has a spectral expansion which decomposes the operator into the point spectrum (eigenvalues) and their associated (Koopman) modes and the continuous spectrum [4]}, [5]}, [8]}. Much recent work has been done on algorithms that compute an approximation of the point spectrum of the Koopman operator [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}. These methods are purely data-driven and are based off computing a spectral decomposition of the Koopman operator without requiring a concrete representation of the operator.
